Landslide monitoring data processing method and system based on time sequence matrix completion

Abstract

The invention discloses a landslide monitoring data processing method and system based on time sequence matrix completion, particularly relates to the technical field of data completion and machine learning, and is used for solving the problem of uncertainty evaluation distortion of a downstream early warning model caused by output of a deterministic value in an existing completion method. The method comprises the steps of obtaining a time sequence observation matrix containing missing values, dividing missing position subsets according to a missing mode, determining a differentiated completion uncertainty evaluation criterion in combination with a time evolution stage of landslide deformation, and further generating completion uncertainty measurement of each subset based on time-space neighborhood data consistency. And finally, iterative weighted completion is carried out according to the measurement, and a complete data matrix with quantitative uncertainty information attached to each completion value is output.

Description

Technical Field

[0001] This invention relates to the fields of data completion and machine learning technology, and more specifically, to a method and system for processing landslide monitoring data based on time series matrix completion. Background Technology

[0002] In the field of landslide monitoring, continuous observation of multiple sensor nodes deployed on the slope surface yields time-series data reflecting the slope's deformation state. This time-series data often suffers from varying degrees of loss due to natural geographical environment and equipment factors, resulting in a time-series data matrix with missing values. Time-series matrix completion techniques can be used to estimate these missing values ​​and restore data integrity. Existing completion methods aim to learn spatiotemporal correlations from known observation data and calculate a specific estimate for each missing location, thereby generating a complete data matrix that can be used for subsequent landslide stability assessment and early warning models.

[0003] However, when it comes to the decision-making task of landslide early warning, the essence of landslide early warning is to conduct risk assessment and decision-making based on incomplete and noisy observation information. The effectiveness of its decision-making model (especially the probability-based machine learning model) depends on the accurate quantification of the uncertainty of the data itself and the model inference. Existing technology treats the completion process as an independent data repair link. Its output deterministic completion value masks the estimation uncertainty introduced by the missing data. When these complete data, which are regarded as accurate, are input into the downstream early warning model, they will distort the uncertainty propagation and evaluation mechanism inside the model, resulting in a distortion of the credibility assessment of the early warning signal. This causes a mismatch between the goal of the data processing stage and the needs of the final application stage, weakening the decision reliability of the entire monitoring and early warning system. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, the present invention provides a landslide monitoring data processing method and system based on time series matrix completion to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] The landslide monitoring data processing method based on time series matrix completion includes the following steps:

[0007] S1. Obtain a time series observation matrix containing missing values, formed by continuous time series observations from multiple landslide monitoring points;

[0008] S2. Extract the positions of all missing values ​​from the time series observation matrix to form a set of missing positions, and divide the set of missing positions according to the missing pattern of the time series observation matrix to obtain multiple subsets of missing positions.

[0009] S3. Based on the existing observation sequence in the time series observation matrix, identify the current time evolution stage of landslide deformation;

[0010] S4. Determine the corresponding criteria for assessing the uncertainty of completion based on the current time evolution stage;

[0011] S5. Based on the consistency of the existing observations in the spatiotemporal neighborhood of the missing location subset in the time series observation matrix, and according to the completion uncertainty assessment criterion, generate the completion uncertainty measure of the missing location subset.

[0012] S6. Iteratively complete the time series observation matrix based on the completion uncertainty metric. During the iteration process, dynamically adjust the completion attention weight for different missing position subsets, and finally generate and output a complete landslide monitoring data matrix with uncertainty quantification information.

[0013] Furthermore, S1 includes:

[0014] Acquire raw observation data collected at continuous time points by multiple monitoring sensors deployed on the surface of the landslide;

[0015] In the time series observation matrix, each row corresponds to a landslide monitoring point, and each column corresponds to a continuous time point. The element values ​​in the time series observation matrix include the original observation data and the missing values ​​caused by data loss.

[0016] Furthermore, S2 includes:

[0017] Scan the time series observation matrix to identify the landslide monitoring point identifier and observation time point identifier corresponding to each missing value;

[0018] The combination of all identified landslide monitoring point identifiers and observation time point identifiers is used to construct a set of missing locations;

[0019] Based on the spatial proximity and temporal continuity of each missing value in the missing location set within the time series observation matrix, the missing location set is divided into multiple missing location subsets.

[0020] Furthermore, S3 includes:

[0021] Effective observation data along the time dimension of each landslide monitoring point are extracted from the time series observation matrix to form the existing observation value sequence of each landslide monitoring point.

[0022] The existing observation sequence of each landslide monitoring point is analyzed, and its deformation rate and trend within the preset time window are calculated.

[0023] Based on a comprehensive assessment of the deformation rate and trend at all landslide monitoring points, the current time evolution stage of landslide deformation is identified as one of the following: initial deformation stage, isochronous deformation stage, or accelerated deformation stage.

[0024] Furthermore, S4 includes:

[0025] Establish a mapping relationship between the time evolution stages and the uncertainty assessment criteria. The time evolution stages include the initial deformation stage, the constant-rate deformation stage, and the accelerated deformation stage.

[0026] Based on the identified current time evolution stage, the corresponding completion uncertainty assessment criteria are selected from the mapping relationship.

[0027] Furthermore, the uncertainty tolerance of the completion uncertainty assessment criterion selected for the accelerated deformation stage is lower than that of the completion uncertainty assessment criterion selected for the constant velocity deformation stage or the initial deformation stage.

[0028] Furthermore, S5 includes:

[0029] For each subset of missing locations, determine its corresponding spatial neighborhood radius and time window length in the time series observation matrix;

[0030] Within the range defined by the spatial neighborhood radius and the time window length, extract all existing observations;

[0031] Calculate the statistical dispersion of the extracted existing observations as the degree of consistency of existing observations in the spatiotemporal neighborhood corresponding to the missing location subset;

[0032] Based on the inconsistency tolerance threshold set in the completion uncertainty assessment criteria, the statistical dispersion is mapped to the corresponding completion uncertainty measure.

[0033] Furthermore, S6 includes:

[0034] Based on the completion uncertainty measure of each missing position subset, calculate its corresponding weight adjustment coefficient during the iterative completion process;

[0035] In each iteration of the completion process, the missing values ​​in each missing position subset are updated and estimated using weighted adjustment coefficients calculated at the current time.

[0036] When the iterative completion process meets the preset convergence condition, a completion value is generated for each missing position based on the final estimated value. The completion uncertainty measure of the missing position subset to which the missing position belongs is used as the uncertainty quantification information of the completion value, and together they are output to form a complete landslide monitoring data matrix.

[0037] Furthermore, subsets of missing positions with higher uncertainty in completion are assigned larger weight adjustment coefficients.

[0038] On the other hand, the present invention provides a landslide monitoring data processing system based on time series matrix completion, comprising the following modules:

[0039] The matrix acquisition module is used to acquire a time series observation matrix containing missing values, formed by continuous time series observations from multiple landslide monitoring points.

[0040] The subset acquisition module is used to extract the positions of all missing values ​​from the time series observation matrix, form a set of missing positions, and divide the set of missing positions according to the missing pattern of the time series observation matrix to obtain multiple subsets of missing positions;

[0041] The stage identification module is used to identify the current time evolution stage of landslide deformation based on the existing observation sequence in the time series observation matrix;

[0042] The criteria determination module is used to determine the corresponding criteria for completing uncertainty assessment based on the current time evolution stage;

[0043] The metric generation module is used to generate a metric for the completion uncertainty of the missing location subset based on the consistency of the existing observations in the spatiotemporal neighborhood corresponding to the missing location subset in the time series observation matrix and according to the completion uncertainty assessment criteria.

[0044] The matrix output module is used to iteratively complete the time series observation matrix based on the completion uncertainty metric. During the iteration process, the completion attention weights for different missing location subsets are dynamically adjusted, and finally, a complete landslide monitoring data matrix with uncertainty quantification information is generated and output.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] 1. By deeply coupling and coordinating the data completion process with the uncertainty quantification process of the completion result, the fundamental problem of the distortion of uncertainty assessment in downstream early warning models caused by the output of deterministic values ​​in traditional completion technology is effectively solved. First, the spatiotemporal distribution of missing patterns is finely identified and divided, and the stage characteristics of landslide deformation evolution are combined simultaneously. Thus, different uncertainty assessment criteria are adaptively matched for missing data groups with different spatiotemporal attributes and different risk levels. Instead of directly generating a single completion estimate, a completion uncertainty metric that characterizes the estimation reliability of each group of missing data is pre-calculated based on the degree of local data consistency and the aforementioned criteria. The uncertainty information introduced by data missingness is captured and made explicit at the source.

[0047] 2. It can more accurately characterize the noise structure of the input data, thereby more realistically reflecting the uncertainty at the data level in its internal probability calculation or decision-making logic. When outputting the early warning signal, it can provide a more reliable credibility assessment that matches the quality of its input data, ensuring the structural consistency of the data format produced in the data processing stage, and significantly enhancing the scientific nature and reliability of the entire landslide monitoring and early warning system. Attached Figure Description

[0048] Figure 1 This is a flowchart of the landslide monitoring data processing method based on time series matrix completion according to the present invention;

[0049] Figure 2 This is a schematic diagram of the landslide monitoring data processing system based on time series matrix completion according to the present invention. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0051] Example 1: Figure 1 The present invention provides a landslide monitoring data processing method based on time series matrix completion, which includes the following steps:

[0052] S1. Obtain a time series observation matrix containing missing values, formed by continuous time series observations from multiple landslide monitoring points;

[0053] S2. Extract the positions of all missing values ​​from the time series observation matrix to form a set of missing positions, and divide the set of missing positions according to the missing pattern of the time series observation matrix to obtain multiple subsets of missing positions.

[0054] S3. Based on the existing observation sequence in the time series observation matrix, identify the current time evolution stage of landslide deformation;

[0055] S4. Determine the corresponding criteria for assessing the uncertainty of completion based on the current time evolution stage;

[0056] S5. Based on the consistency of the existing observations in the spatiotemporal neighborhood of the missing location subset in the time series observation matrix, and according to the completion uncertainty assessment criterion, generate the completion uncertainty measure of the missing location subset.

[0057] S6. Iteratively complete the time series observation matrix based on the completion uncertainty metric. During the iteration process, dynamically adjust the completion attention weight for different missing position subsets, and finally generate and output a complete landslide monitoring data matrix with uncertainty quantification information.

[0058] S1. Obtain a time-series observation matrix containing missing values, formed by continuous time-series observations from multiple landslide monitoring points. The specific implementation is as follows:

[0059] On the surface of the landslide requiring monitoring, multiple monitoring sensors are deployed according to the potential deformation areas and key locations identified by engineering surveys. These sensors include GPS receivers for measuring three-dimensional displacement and inclinometers for measuring tilt angles. For example, in a specific landslide monitoring scenario, 20 GPS receivers are deployed along the main sliding direction and both sides of the landslide, and inclinometers are deployed at 10 key geological structural points. All monitoring sensors continuously and automatically observe at preset fixed time intervals, synchronized with a unified clock. This time interval is typically set based on the landslide deformation rate and monitoring requirements, for example, data is collected once per hour. The raw observation data collected by each monitoring sensor at each observation point includes longitude, latitude, and elevation coordinates for the GPS receivers, and tilt angle values ​​along a preset axis for the inclinometers. This raw observation data is transmitted to a data center for aggregation in real time or periodically via wired or wireless transmission networks. In actual observation, raw observation data may be missing because natural geographical factors such as satellite signal obstruction and atmospheric interference, or equipment factors such as sensor power outages and communication link failures may prevent the acquisition of effective data for specific landslide monitoring points at certain observation times.

[0060] A time-series observation matrix is ​​constructed based on the collected raw observation data. Specifically, each landslide monitoring point is uniquely mapped to a row in the time-series observation matrix. For example, the first landslide monitoring point corresponds to the first row of the matrix, the second landslide monitoring point corresponds to the second row, and so on, with the total number of rows equal to the total number of landslide monitoring points. Simultaneously, each consecutive observation time point is uniquely mapped to a column in the time-series observation matrix according to its chronological order. For example, the first observation time point corresponds to the first column, the second observation time point corresponds to the second column, and so on, with the total number of columns equal to the total number of observation periods from the start of monitoring to the current moment. In the time-series observation matrix, the element value located at the intersection of a specific row and a specific column corresponds to the observation result of the landslide monitoring point represented by that row at the observation time point represented by that column. For observation points and time points where raw observation data was successfully acquired, this element value is the specific raw observation data value collected, such as specific coordinate values ​​or tilt angle values. For observation points and time points where data is missing due to the aforementioned reasons, the element value is assigned a specific identifier to indicate the missing data. This identifier is a predefined value that differs from the range of all valid observation data values. For example, in a displacement coordinate scenario, a very large negative value far exceeding the possible displacement range can be used, or in a tilt angle scenario, an impossible angle value such as -360 degrees can be used to explicitly indicate that the location is a missing value. Through the above process, a time series observation matrix is ​​finally formed, with the number of rows equal to the number of landslide monitoring points and the number of columns equal to the number of observation time points. The matrix elements consist of valid original observation data and the specific identifier representing the missing data. This matrix serves as the basic input data for all subsequent data processing steps.

[0061] S2. Extract the locations of all missing values ​​from the time series observation matrix to form a set of missing locations. Then, divide the set of missing locations according to the missing pattern of the time series observation matrix to obtain multiple subsets of missing locations. The specific implementation is as follows:

[0062] The process begins by systematically scanning the time-series observation matrix generated in the previous steps to precisely identify the specific location of each missing value. This scanning process involves traversing each matrix element row by row and column by column, comparing the value of each element with a predefined identifier used to identify missing data. When the value of a matrix element is determined to be equal to the missing value identifier, a missing value is confirmed at that location. At this point, the row index number of the missing value and the unique landslide monitoring point identifier corresponding to that row are recorded. This identifier is typically a sequence number pre-assigned to each landslide monitoring point when constructing the time-series observation matrix, such as an integer number starting from 1 and incrementing sequentially, to uniquely represent that monitoring point. Simultaneously, the column index number of the missing value and the unique observation time point identifier corresponding to that column are recorded. This identifier is typically a sequence number assigned according to the observation time order when constructing the matrix, such as an integer number starting from 1 and incrementing sequentially, to represent the chronological order of the observation times. By traversing the entire time-series observation matrix, the identification of all missing values ​​and their corresponding landslide monitoring point identifiers and observation time point identifiers can be completed.

[0063] After identifying all missing locations, the missing location set is constructed. Specifically, the landslide monitoring point identifier and observation time point identifier corresponding to each missing value identified in the previous step are paired and combined to form an independent location coordinate pair. For example, if the data for the 5th landslide monitoring point is missing at the 10th observation time point, a specific missing location represented by the identifier pair 5 and 10 is generated. All such identifier pairs together constitute the missing location set, which can be in the form of a list or array, where each element is an identifier pair representing a specific missing location. This missing location set completely records the spatial and temporal location information of all missing data points in the entire time series observation matrix.

[0064] Based on the established set of missing locations, the set is partitioned into multiple subsets of missing locations according to the spatial proximity and temporal continuity characteristics of each missing value in the original time-series observation matrix. The partitioning process first requires defining and determining the spatial proximity characteristic. Spatial proximity refers to the degree of closeness of missing locations in a spatial dimension, and its determination is based on the continuity or geographical correlation between the landslide monitoring point identifiers corresponding to the missing locations. In specific implementation, a spatial proximity distance threshold is set to quantify the judgment of spatial proximity. The acquisition and setting of this spatial proximity distance threshold depends on the actual layout of the landslide monitoring points. For example, a specific physical distance value, such as 50 meters, can be set as the spatial proximity distance threshold based on the average or minimum layout spacing between all landslide monitoring points. This means that if the physical distance between the landslide monitoring points corresponding to two missing locations in actual space is less than or equal to 50 meters, they are determined to meet the spatial proximity condition. Another optional approach is to directly set a threshold for the numbering of landslide monitoring points as a proxy for the spatial proximity threshold when the numbers roughly reflect the spatial relationships. For example, a threshold of 3 could be set for the numbering difference. This means that if the absolute value of the difference between the numbering of landslide monitoring points corresponding to two missing locations is less than or equal to 3, they are considered to meet the spatial proximity condition. The specific method and threshold value to be used need to be determined based on the specific layout characteristics of the monitoring network, with the core principle being that it should reasonably reflect the spatial clustering characteristics of the monitoring points.

[0065] The segmentation process also requires defining and judging the temporal continuity characteristic. Temporal continuity refers to the degree of continuity of missing locations in the time dimension, and its judgment is based on the continuity between the observation time point identifiers corresponding to the missing locations. In specific implementation, a temporal continuity threshold is set to quantify the judgment of temporal continuity. The acquisition and setting of this temporal continuity threshold depends on the sampling frequency of the observation data and the time scale characteristics of landslide deformation. For example, a specific time window length can be set as the temporal continuity threshold based on the time interval of the observation data and the stage duration of the landslide deformation process. If the observation time interval is 1 hour, and it is desired to classify missing locations occurring within several consecutive observation periods as having temporal continuity, then the temporal continuity threshold can be set to 3 observation time points, i.e., 3 consecutive hours. This means that if the observation time point identifiers corresponding to two missing locations are consecutive integers, or the number of observation periods between them is less than or equal to 2 (i.e., the time interval is within 2 hours), then they are determined to meet the temporal continuity condition. Another setting method is to directly use the physical time length, for example, setting the temporal continuity threshold to 6 hours. The specific threshold setting needs to balance the sensitivity to identify long-term persistent missing patterns with the ability to distinguish short-term random missing patterns.

[0066] The specific implementation logic of the partitioning operation is as follows, which comprehensively utilizes the aforementioned spatial proximity threshold and temporal continuity threshold. Starting from a missing location pair that has not yet been partitioned into any subset, a new missing location subset is created and added. Then, all other remaining pair of identifiers in the missing location set are examined to find missing locations that simultaneously satisfy the following two conditions with any pair of identifiers in the current subset: First, spatially, the landslide monitoring points corresponding to the two missing locations satisfy the proximity judgment based on the spatial proximity threshold; second, temporally, the observation time points corresponding to the two missing locations satisfy the continuity judgment based on the temporal continuity threshold. If such a pair of identifiers is found, it is added to the current missing location subset. This process iterates continuously, checking the spatial and temporal relationships between newly added pair of identifiers and the remaining pair of identifiers in the set, until no new pair of identifiers simultaneously satisfies the proximity and continuity conditions with any member of the current subset. At this point, the construction of a missing location subset is complete. Subsequently, a new starting point is selected from the remaining label pairs in the missing location set, and the above threshold-based spatial proximity and temporal continuity judgment and clustering addition process is repeated to construct the next missing location subset. This process is repeated until all label pairs in the missing location set are assigned to a certain missing location subset. Ultimately, the original complete missing location set is divided into several missing location subsets. The missing locations within each subset are relatively concentrated in spatial distribution and relatively continuous in temporal occurrence, while the missing locations between different subsets have relatively obvious spatial or temporal intervals. These missing location subsets will serve as the basic units for uncertainty assessment and differential completion processing in subsequent steps.

[0067] S3. Based on the existing observation sequence in the time series observation matrix, identify the current time evolution stage of the landslide deformation. The specific implementation is as follows:

[0068] The process begins by extracting valid observation data along the time dimension for each landslide monitoring point from the time-series observation matrix generated in the previous steps. During extraction, for each row of the time-series observation matrix, corresponding to a specific landslide monitoring point, each matrix element is examined sequentially along the column direction, i.e., the time dimension. Only matrix elements whose values ​​do not equal predefined missing value identifiers are identified as valid observation data. These valid observation data are then arranged in chronological order according to their corresponding observation time point identifiers, forming a numerical sequence arranged in chronological order, which is the existing observation value sequence for that landslide monitoring point. For example, for a monitoring point with 50 observation time points, if the data for the 10th and 20th time points are missing values, the extracted existing observation value sequence will consist of the remaining 48 valid observation data arranged in chronological order. This extraction process is performed independently for each row of the time-series observation matrix, thus generating a corresponding existing observation value sequence for each landslide monitoring point.

[0069] After obtaining the existing observation sequences for each landslide monitoring point, each sequence is analyzed independently to calculate its deformation rate and trend within a preset time window. The preset time window is a key parameter; its length defines the most recent time range of interest in the analysis. The acquisition and setting of the preset time window depends on the timescale characteristics of the landslide deformation process and the frequency of data collection. For example, if the observation data is collected hourly, and the focus is on the landslide's dynamics over the past few days to weeks, the preset time window can be set to include the most recent 72 observation points, corresponding to the observation data of the most recent 3 days. Specifically, the window length should be sufficient to include multiple data points that reflect the deformation trend, but not so long as to fail to accurately reflect the latest changes. For each existing observation sequence at a landslide monitoring point, the analysis focuses on the last observation data point in the sequence that falls within the preset time window and several consecutive data points preceding it. The calculation of the deformation rate aims to quantify the speed at which deformation occurs. One specific implementation involves calculating the difference between the last valid observation value and the first valid observation value within a preset time window, and then dividing this difference by the actual time interval between these two observations. Trend analysis aims to determine whether the deformation rate increases, decreases, or remains essentially constant within the preset time window. One specific implementation involves linearly fitting all valid observation data sequences within the preset time window to obtain a fitted straight line. The slope of this fitted line characterizes the direction and intensity of the trend. A positive slope indicates an upward trend over time, while a negative slope indicates a downward trend; the absolute value of the slope reflects the strength of the trend. Another simplified implementation involves calculating the average rate of change of the data points in the latter half of the window and comparing them with the average rate of change of the data points in the first half, to determine whether the rate of change is accelerating, decelerating, or remaining stable.

[0070] The current time evolution stage of the overall landslide deformation is identified by comprehensively judging the deformation change rate and trend of all landslide monitoring points. This requires aggregate analysis and logical judgment of the change rate and trend information calculated from all monitoring points. First, threshold parameters for stage discrimination are set, including a change rate threshold and a trend intensity threshold. The change rate threshold is used to distinguish significant deformation activity from background noise or a stable state. It can be obtained based on the statistical characteristics of the change rate during the stable period of the landslide in historical observation data. For example, three times the standard deviation of the change rate during the historical stable period can be set as the change rate threshold. The trend intensity threshold is used to confirm the significance of the trend. It can be obtained based on the statistical test results of linear fitting or based on empirical values. For example, a specific lower limit of the absolute value of the slope can be set as the trend intensity threshold. The comprehensive judgment follows a set of predefined logical rules. For example, rule one is the initial deformation stage judgment rule: when the absolute value of the deformation change rate of most of the landslide monitoring points exceeds 70% of the monitoring points below the preset change rate threshold, and the change trend of each point is not obvious, that is, the trend intensity is lower than the trend intensity threshold, it is determined that the current stage is the initial deformation stage. Rule Two is the determination rule for the isochronous deformation stage: When a considerable proportion, for example, more than 50% of the landslide monitoring points have an absolute value of deformation rate of change higher than the rate of change threshold, and although the intensity of the change trend of these monitoring points is higher than the threshold, the change rate values ​​fluctuate within a small range, for example, the fluctuation range is less than 20% of the average rate of change, and no systematic and consistent acceleration or deceleration pattern is shown, the current stage is determined to be isochronous deformation. Rule Three is the determination rule for the accelerated deformation stage: When a significant proportion, for example, more than 50% of the landslide monitoring points not only have an absolute value of deformation rate of change higher than the rate of change threshold, but their change trend also shows a systematic and consistent positive acceleration (i.e., the fitting slope is positive and exceeds the trend intensity threshold) or negative acceleration, and this acceleration trend has a certain degree of spatial correlation (e.g., multiple spatially adjacent monitoring points all show acceleration), the current stage is determined to be accelerated deformation. These rules are applied sequentially; a determination is made when the conditions of a certain stage are met. If all rules are not met, the current stage can be conservatively determined, or a more in-depth review is required. Through the above process, the current time evolution stage of the landslide deformation is finally identified as one of the initial deformation stage, the isostatic deformation stage, or the accelerated deformation stage. This identification result provides a direct basis for the adaptive selection and completion of the uncertainty assessment criteria in subsequent steps.

[0071] S4. Determine the corresponding uncertainty assessment criteria based on the current time evolution stage, specifically as follows:

[0072] The process first requires establishing a clear mapping relationship between the time evolution stages and the completion uncertainty assessment criteria. The time evolution stages adopt the types identified in the previous steps: the initial deformation stage, the constant-rate deformation stage, and the accelerated deformation stage. The completion uncertainty assessment criteria are specifically defined here as a set of parameters and rules used to quantify and evaluate the reliability of the data completion results in subsequent steps. The core of establishing the mapping relationship lies in pre-configuring a unique set of parameters for each specific time evolution stage; this set of parameters directly constitutes the completion uncertainty assessment criteria for that stage. In practice, the mapping relationship can be represented as a predefined lookup table or logical mapping rules, stored in a configuration file or as conditional statements built into the processing logic.

[0073] The uncertainty assessment criteria configured for the initial deformation stage focus on maintaining the stability of the completion process even when data fluctuations or noise exist. For example, a relatively lenient inconsistency tolerance threshold can be set for this stage. This threshold can be obtained and set based on statistical analysis of the natural fluctuation range of effective observation data within the stable or initial deformation stages of historical data. For instance, the standard deviation of the deviations between all effective observation data points and their local means during this historical period can be calculated, and two to three times this standard deviation can be set as the inconsistency tolerance threshold. This means that in subsequent evaluations, when the dispersion of data surrounding the location to be completed is lower than this threshold, the completion uncertainty is considered low. Simultaneously, a higher base value for data reliability weighting can be set for this stage, such as 0.8, indicating a greater tendency to rely on and depend on existing surrounding observation data during completion.

[0074] The uncertainty assessment criteria configured for the constant-rate deformation stage must balance stability with sensitivity to deformation trends. The inconsistency tolerance threshold for this stage should be more stringent than that for the initial deformation stage, and can be recalibrated based on the rate of change and fluctuation characteristics of historical data from the constant-rate deformation stage. For example, a smaller threshold can be set using a multiple of the standard deviation of the historical data rate of change series for this stage, such as 2.5 times, to reduce tolerance for data fluctuations. The base value for data reliability weighting may be set at a moderate level, such as 0.6, reflecting a balance between trust and caution when dealing with relatively stable trends.

[0075] The completion uncertainty assessment criteria configured for the accelerated deformation stage have the most stringent parameter settings, aiming to capture and warn of data completion risks that may significantly increase due to accelerated deformation. The inconsistency tolerance threshold for this stage should be set to the most stringent of the three, i.e., the lowest value. This threshold needs to be obtained based on typical data characteristics of the accelerated deformation stage, such as analyzing the data dispersion when trends change drastically or outliers appear in historical data during this stage, setting an extremely low threshold, such as one time or even less than the standard deviation of historical data. This directly reflects its lower uncertainty tolerance compared to other stages. Simultaneously, the basic value for data reliability weighting may be set to a low value, such as 0.4, indicating that in this high-risk stage, the reliability of single-location or short-time-series data is reduced, requiring broader cross-validation using spatiotemporal information. Furthermore, the criteria for the accelerated deformation stage may include an additional rule: when the calculated preliminary uncertainty measure exceeds a preset extremely high-risk threshold, regardless of other parameters, the completion task is directly marked as the highest uncertainty level. This extremely high-risk threshold can be set based on the engineering safety tolerance limit error or the analysis of data characteristics before historical incidents.

[0076] After establishing the mapping relationship and configuring the parameters, determining the corresponding criteria becomes a direct query or matching operation. Specifically, based on the current time evolution stage output from the previous identification step, the system uses the current time evolution stage as an input key. Then, it searches within the established mapping relationship. If the mapping relationship exists in the form of a lookup table, the system retrieves and reads the corresponding complete set of parameters by matching the current time evolution stage with the pre-stored stage names in the table. These parameters constitute the completion uncertainty assessment criteria to be used. If the mapping relationship is encoded in the form of logical rules, the system determines which conditional branch the current time evolution stage satisfies, and then performs parameter assignment operations under that branch to generate the corresponding completion uncertainty assessment criteria. For example, if the current time evolution stage is an accelerated deformation stage, the system automatically selects and activates a set of criteria preset for that stage, with strict parameters such as a minimum inconsistency tolerance threshold and a low data credibility weight base value. Through this process, it ensures that appropriate, risk-matched assessment criteria are assigned to data completion tasks under different deformation states, laying the foundation for subsequent accurate quantification of completion uncertainty.

[0077] S5. Based on the consistency of existing observations in the spatiotemporal neighborhood corresponding to the missing location subset in the time series observation matrix, and according to the completion uncertainty assessment criterion, a completion uncertainty measure for the missing location subset is generated. Specifically, the implementation is as follows:

[0078] This process is performed independently and sequentially for each subset of missing locations obtained in the previous steps. First, for the currently processed subset of missing locations, its corresponding spatial neighborhood radius and time window length in the time-series observation matrix need to be determined. The spatial neighborhood radius defines the spatial range in the missing location subset, centered on the landslide monitoring point, from which relevant existing observations are searched for. The specific acquisition and setting of the spatial neighborhood radius depends on the actual deployment density and spatial correlation scale of the landslide monitoring points. For example, a specific physical distance can be determined as the spatial neighborhood radius by multiplying the average or median distance between all adjacent monitoring points in the monitoring network by an empirical coefficient. If the average spacing between monitoring points is 20 meters, and the empirical coefficient can be 1.5, then the spatial neighborhood radius can be set to 30 meters. This means that for any missing location in the subset of missing locations corresponding to a landslide monitoring point, a circular planar area with a radius of 30 meters centered on that location is defined as the spatial neighborhood of that point. The time window length defines the time range within which, centered on the observation time points contained in the subset of missing locations, a search is conducted in both forward and backward directions to obtain relevant existing observations. The specific acquisition and setting of the time window length depends on the frequency of observation data acquisition and the temporal continuity of the landslide deformation process. For example, if observation data is acquired hourly, and the goal is to analyze the correlation of data from the most recent hours to one day, the time window length can be set to include the current observation time point and five time points before and after it, totaling a five-hour time span. The spatial neighborhood radius and the time window length together define a three-dimensional spatiotemporal columnar search range centered on each missing location.

[0079] After defining the spatial neighborhood radius and time window length, for each specific missing location in the current subset of missing locations, all existing observations are extracted from the time series observation matrix according to the defined spatiotemporal search range. Specifically, for the landslide monitoring point identifier corresponding to the missing location, all other landslide monitoring points with a spatial distance less than or equal to the spatial neighborhood radius are identified; these points constitute the spatial neighborhood point set. Simultaneously, for the observation time point identifier corresponding to the missing location, all other observation time points with a time interval less than or equal to half the time window length are identified; these points constitute the temporal neighborhood point set. Next, in the time series observation matrix, for each monitoring point in the spatial neighborhood point set and each time point in the temporal neighborhood point set, the matrix element value at the intersection is checked. If the element value is not equal to the predefined missing value identifier, it is identified as a valid existing observation value, and its value is recorded. This operation is applied to all missing locations in the current subset of missing locations, and the valid existing observations extracted from all locations are aggregated to form a numerical set. This set represents all available valid data within the spatiotemporal neighborhood associated with the missing location subset.

[0080] Based on the extracted set of existing observations, the statistical dispersion is calculated, and this statistical dispersion is used as the degree of consistency among existing observations in the spatiotemporal neighborhood corresponding to the missing location subset. Statistical dispersion is a statistic that measures the degree of dispersion of a set of data. A commonly used calculation method is standard deviation. The specific calculation steps are as follows: first, calculate the arithmetic mean of all existing observations in the set; then, calculate the difference between each existing observation and this arithmetic mean; next, square each difference; then, calculate the mean of all these squared values; finally, take the square root of this mean, and the result is the standard deviation, which has the same dimensions as the original observed data, such as millimeters or degrees. Another available calculation method is mean absolute deviation, which calculates the absolute value of the difference between each existing observation and the arithmetic mean, and then calculates the average of these absolute values. The larger the statistical dispersion value, the greater the numerical difference between the extracted existing observations, i.e., the lower the degree of consistency; conversely, the smaller the value, the closer the observations are, i.e., the higher the degree of consistency.

[0081] Based on the completion uncertainty assessment criteria determined in the previous steps according to the current time evolution stage, the calculated statistical dispersion is mapped to the corresponding completion uncertainty metric. One key parameter in this completion uncertainty assessment criterion is the inconsistency tolerance threshold, which has been set in the criterion according to the risk characteristics of the current stage. The core of the mapping process is to compare the statistical dispersion with this inconsistency tolerance threshold and generate a quantified uncertainty metric value according to predetermined rules. A specific mapping implementation method is to set a linear or piecewise linear function. For example, when the statistical dispersion is less than or equal to the inconsistency tolerance threshold, the uncertainty is considered low, and the completion uncertainty metric can be directly set to a low fixed value, such as 0.1. When the statistical dispersion is greater than the inconsistency tolerance threshold, the uncertainty is considered to increase with increasing dispersion. In this case, the completion uncertainty metric can be calculated as (statistical dispersion - inconsistency tolerance threshold) / inconsistency tolerance threshold, and then the calculation result is limited to the range of 0 to 1 as the final uncertainty metric. Another mapping method is to use a lookup table. This involves pre-dividing the statistical dispersion into several intervals based on an inconsistency tolerance threshold, and assigning a specific uncertainty metric level to each interval. For example, three intervals can be set: a low uncertainty interval where the statistical dispersion is less than or equal to 50% of the inconsistency tolerance threshold, with a mapping metric value of 0.2; a medium uncertainty interval where the statistical dispersion is greater than 50% but less than or equal to the inconsistency tolerance threshold, with a mapping metric value of 0.5; and a high uncertainty interval where the statistical dispersion is greater than the inconsistency tolerance threshold, with a mapping metric value of 0.8. Through this process, a specific, quantified completion uncertainty metric is calculated for the currently processed subset of missing locations. This value comprehensively reflects the consistency of the data within its spatiotemporal neighborhood and the risk tolerance requirements of the current deformation stage. Repeating the above complete process for all subsets of missing locations generates a corresponding completion uncertainty metric for each subset.

[0082] S6. Iteratively complete the time series observation matrix based on the uncertainty metric, dynamically adjusting the completion weights for different missing subsets during the iteration process, and finally generating and outputting a complete landslide monitoring data matrix with uncertainty quantification information. The specific implementation is as follows:

[0083] The process first calculates the completion uncertainty metric obtained for each missing location subset in the previous steps, and then calculates its corresponding weight adjustment coefficient during the iterative completion process. The calculation of the weight adjustment coefficient aims to convert the completion uncertainty metric into a positive weight value that directly affects the subsequent completion update magnitude. The basic principle is that missing location subsets with higher completion uncertainty metrics are assigned larger weight adjustment coefficients, giving them more attention and adjustment opportunities during iteration. One specific implementation is to establish a direct proportional relationship between the weight adjustment coefficient and the completion uncertainty metric. For example, the completion uncertainty metric value can be directly used as the initial weight, and then the initial weights of all missing location subsets can be normalized so that the sum of all weight adjustment coefficients is 1. The specific calculation steps for the normalization process are as follows: first, add the completion uncertainty metric values ​​of all missing location subsets to obtain a total; then, divide the completion uncertainty metric value of each missing location subset by this total, and the quotient is the weight adjustment coefficient corresponding to that subset. Another approach is to use an exponential amplification relationship. For example, the weight adjustment coefficient can be calculated as the square of the completed uncertainty measure, and then normalized. This can significantly increase the weight of the high-uncertainty subset. The specific calculation relationship of the weight adjustment coefficient can be selected and set according to the uncertainty sensitivity requirements in the actual application.

[0084] After obtaining the weight adjustment coefficients corresponding to each missing location subset, an iterative completion process for the time series observation matrix is ​​initiated. Iterative completion requires a pre-defined convergence condition to terminate the iteration. The convergence condition typically includes a maximum iteration threshold and an estimate change threshold. The maximum iteration threshold is determined based on a balance between computational efficiency and accuracy; for example, it can be preset to 100 iterations. The estimate change threshold is used to determine whether the estimate has stabilized; its determination can be based on the accuracy requirements of the completed value, for example, preset to 0.01 mm. At the start of the iteration process, an initial estimate needs to be provided for all missing values ​​in the time series observation matrix. The initial estimate can be simply the average of all existing observations in its spatiotemporal neighborhood, or the observation value from the same monitoring point at the previous observation time point. In each iteration, based on the currently calculated weight adjustment coefficients, a weighted update estimate is performed for each missing value in each missing location subset. The specific operation of the weighted update estimate is as follows: for each missing location, firstly, based on its corresponding missing location subset, obtain the weight adjustment coefficients for that subset. Then, calculate the candidate update value for that missing location in the current iteration. The candidate update value can be calculated based on a weighted average of existing observations within the spatiotemporal neighborhood of the missing location, where weights can be allocated according to spatial distance and time interval. Next, the old estimate for the current missing location is adjusted towards the candidate update value, but the adjustment step size is controlled by the weight adjustment coefficient. Specifically, the new estimate can be calculated as follows: the new estimate equals the old estimate plus the weight adjustment coefficient multiplied by the candidate update value minus the old estimate. This means that for missing values ​​within a subset of missing locations with a high weight adjustment coefficient, the estimate will move closer to the candidate update value with a larger step size in each iteration, resulting in a more proactive correction; while for subsets with low weight adjustment coefficients, the estimate update is more conservative and slower. This update process is performed in parallel or sequentially for all missing locations in one iteration, completing one global update.

[0085] The iterative process continues. After each iteration, the preset convergence condition is checked. The maximum number of iterations is checked to see if it has reached a preset threshold (e.g., the current iteration count has reached 100). Simultaneously, the absolute value of the difference between the new estimate for all missing positions and the old estimate from the previous iteration is calculated. The maximum value is identified, and it is determined whether this maximum value is less than a preset threshold for estimate change (e.g., less than 0.01 mm). If the current iteration count has reached the maximum threshold, or the maximum change in all missing value estimates is less than the threshold, the iterative completion process is considered to have met the convergence condition, and the iteration stops. If not, the new estimate obtained in this round of updates is used as the old estimate for the next round, and the weighted update estimation steps are repeated until the convergence condition is met.

[0086] When the iterative completion process terminates upon meeting the convergence condition, a completed value is generated for each missing location based on the final estimate. Specifically, each missing value identifier in the time series observation matrix is ​​replaced with the new estimate obtained after the last iteration for the corresponding missing location; this value is the final completed value. Simultaneously, uncertainty quantification information needs to be associated with the completed value. For each missing location, the completion uncertainty metric calculated before iteration for its subset of missing locations is obtained, and this metric is used as the uncertainty quantification information for the completed value at that location. Finally, a complete landslide monitoring data matrix is ​​generated and output. This complete matrix has the same number of rows and columns as the original time series observation matrix, with the original valid observations remaining unchanged, and all the original missing locations replaced by completed values. Furthermore, each completed value is associated with a corresponding completion uncertainty metric, which is output synchronously with the completed value as an additional data segment or an independent matrix, together forming a complete landslide monitoring data matrix with uncertainty quantification information, providing a complete and quality-controlled data foundation for subsequent landslide stability analysis and early warning.

[0087] Example 2: Figure 2 A schematic diagram of the landslide monitoring data processing system based on time series matrix completion of the present invention is given. The landslide monitoring data processing system based on time series matrix completion includes the following modules:

[0088] The matrix acquisition module is used to acquire a time series observation matrix containing missing values, formed by continuous time series observations from multiple landslide monitoring points.

[0089] The subset acquisition module is used to extract the positions of all missing values ​​from the time series observation matrix, form a set of missing positions, and divide the set of missing positions according to the missing pattern of the time series observation matrix to obtain multiple subsets of missing positions;

[0090] The stage identification module is used to identify the current time evolution stage of landslide deformation based on the existing observation sequence in the time series observation matrix;

[0091] The criteria determination module is used to determine the corresponding criteria for completing uncertainty assessment based on the current time evolution stage;

[0092] The metric generation module is used to generate a metric for the completion uncertainty of the missing location subset based on the consistency of the existing observations in the spatiotemporal neighborhood corresponding to the missing location subset in the time series observation matrix and according to the completion uncertainty assessment criteria.

[0093] The matrix output module is used to iteratively complete the time series observation matrix based on the completion uncertainty metric. During the iteration process, the completion attention weights for different missing location subsets are dynamically adjusted, and finally, a complete landslide monitoring data matrix with uncertainty quantification information is generated and output.

[0094] All calculations involved in the embodiments are dimensionless numerical calculations, and the preset parameters and thresholds in the calculations are set by those skilled in the art according to the actual situation.

[0095] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0096] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and inventive constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0097] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0098] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0099] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0100] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A landslide monitoring data processing method based on time series matrix completion, characterized in that, Includes the following steps: S1. Obtain a time series observation matrix containing missing values, formed by continuous time series observations from multiple landslide monitoring points; S2. Extract the positions of all missing values ​​from the time series observation matrix to form a set of missing positions, and divide the set of missing positions according to the missing pattern of the time series observation matrix to obtain multiple subsets of missing positions. S3. Based on the existing observation sequence in the time series observation matrix, identify the current time evolution stage of landslide deformation; S4. Determine the corresponding criteria for assessing the uncertainty of completion based on the current time evolution stage; S5. Based on the consistency of the existing observations in the spatiotemporal neighborhood corresponding to the missing location subset in the time series observation matrix, and according to the completion uncertainty assessment criterion, generate the completion uncertainty measure of the missing location subset. S6. Iteratively complete the time series observation matrix based on the completion uncertainty metric. During the iteration process, dynamically adjust the completion attention weight for different missing position subsets, and finally generate and output a complete landslide monitoring data matrix with uncertainty quantification information.

2. The landslide monitoring data processing method based on time series matrix completion according to claim 1, characterized in that, S1 includes: Acquire raw observation data collected at continuous time points by multiple monitoring sensors deployed on the surface of the landslide; In the time series observation matrix, each row corresponds to a landslide monitoring point, and each column corresponds to a continuous time point. The element values ​​in the time series observation matrix include the original observation data and the missing values ​​caused by data loss.

3. The landslide monitoring data processing method based on time series matrix completion according to claim 1, characterized in that, S2 include: Scan the time series observation matrix to identify the landslide monitoring point identifier and observation time point identifier corresponding to each missing value; The combination of all identified landslide monitoring point identifiers and observation time point identifiers is used to construct a set of missing locations; Based on the spatial proximity and temporal continuity of each missing value in the missing location set within the time series observation matrix, the missing location set is divided into multiple missing location subsets.

4. The landslide monitoring data processing method based on time series matrix completion according to claim 1, characterized in that, S3 includes: Effective observation data along the time dimension of each landslide monitoring point are extracted from the time series observation matrix to form the existing observation value sequence of each landslide monitoring point. The existing observation sequence of each landslide monitoring point is analyzed, and its deformation rate and trend within the preset time window are calculated. Based on a comprehensive assessment of the deformation rate and trend at all landslide monitoring points, the current time evolution stage of landslide deformation is identified as one of the following: initial deformation stage, isochronous deformation stage, or accelerated deformation stage.

5. The landslide monitoring data processing method based on time series matrix completion according to claim 1, characterized in that, S4 includes: Establish a mapping relationship between the time evolution stages and the uncertainty assessment criteria. The time evolution stages include the initial deformation stage, the constant-rate deformation stage, and the accelerated deformation stage. Based on the identified current time evolution stage, the corresponding completion uncertainty assessment criteria are selected from the mapping relationship.

6. The landslide monitoring data processing method based on time series matrix completion according to claim 5, characterized in that, The uncertainty tolerance of the completion uncertainty assessment criterion selected for the accelerated deformation stage is lower than that selected for the completion uncertainty assessment criterion for the constant velocity deformation stage or the initial deformation stage.

7. The landslide monitoring data processing method based on time series matrix completion according to claim 1, characterized in that, S5 include: For each subset of missing locations, determine its corresponding spatial neighborhood radius and time window length in the time series observation matrix; Within the range defined by the spatial neighborhood radius and the time window length, extract all existing observations; Calculate the statistical dispersion of the extracted existing observations as the degree of consistency of existing observations in the spatiotemporal neighborhood corresponding to the missing location subset; Based on the inconsistency tolerance threshold set in the completion uncertainty assessment criteria, the statistical dispersion is mapped to the corresponding completion uncertainty measure.

8. The landslide monitoring data processing method based on time series matrix completion according to claim 1, characterized in that, S6 include: Based on the completion uncertainty measure of each missing position subset, calculate its corresponding weight adjustment coefficient during the iterative completion process; In each iteration of the completion process, the missing values ​​in each missing position subset are updated and estimated using weighted adjustment coefficients calculated at the current time. When the iterative completion process meets the preset convergence condition, a completion value is generated for each missing position based on the final estimated value. The completion uncertainty measure of the missing position subset to which the missing position belongs is used as the uncertainty quantification information of the completion value, and together they are output to form a complete landslide monitoring data matrix.

9. The landslide monitoring data processing method based on time series matrix completion according to claim 8, characterized in that, The subset of missing positions with higher uncertainty in the completion is assigned a larger weight adjustment coefficient.

10. A landslide monitoring data processing system based on time series matrix completion, used to implement the landslide monitoring data processing method based on time series matrix completion as described in any one of claims 1-9, characterized in that, Includes the following modules: The matrix acquisition module is used to acquire a time series observation matrix containing missing values, formed by continuous time series observations from multiple landslide monitoring points. The subset acquisition module is used to extract the positions of all missing values ​​from the time series observation matrix, form a set of missing positions, and divide the set of missing positions according to the missing pattern of the time series observation matrix to obtain multiple subsets of missing positions; The stage identification module is used to identify the current time evolution stage of landslide deformation based on the existing observation sequence in the time series observation matrix; The criteria determination module is used to determine the corresponding criteria for completing uncertainty assessment based on the current time evolution stage; The metric generation module is used to generate a metric for the completion uncertainty of the missing location subset based on the consistency of the existing observations in the spatiotemporal neighborhood corresponding to the missing location subset in the time series observation matrix and according to the completion uncertainty assessment criteria. The matrix output module is used to iteratively complete the time series observation matrix based on the completion uncertainty metric. During the iteration process, the completion attention weights for different missing location subsets are dynamically adjusted, and finally, a complete landslide monitoring data matrix with uncertainty quantification information is generated and output.

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